Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2022, Volume 18, Issue 2, Pages 198–208
DOI: https://doi.org/10.21638/11701/spbu10.2022.201 (Mi vspui527) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Applied mathematics

Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov — Krasovskii and Razumikhin approaches

S. E. Kuptsovaa, S. Yu. Kuptsovb

a St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
b OOO “OGS Russia”, 21a, Gakkelevskaya ul., St Petersburg, 197227, Russian Federation
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DOI: https://doi.org/10.21638/11701/spbu10.2022.201
Abstract: The nonlinear time-delay systems are considered and the limiting behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov — Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.
Keywords: time-delay systems, asymptotic stability, asymptotic quiescent position, Lyapunov — Krasovskii functionals.
Received: November 19, 2021
Accepted: May 5, 2022
Document Type: Article
UDC: 517.929.4
MSC: 34K20
Language: English
Citation: S. E. Kuptsova, S. Yu. Kuptsov, “Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov — Krasovskii and Razumikhin approaches”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 18:2 (2022), 198–208
Citation in format AMSBIB
\Bibitem{KupKup22}
\by S.~E.~Kuptsova, S.~Yu.~Kuptsov
\paper Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov --- Krasovskii and Razumikhin approaches
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2022
\vol 18
\issue 2
\pages 198--208
\mathnet{http://mi.mathnet.ru/vspui527}
\crossref{https://doi.org/10.21638/11701/spbu10.2022.201}
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    • This publication is cited in the following 1 articles:
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    		Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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